Exploiting Prior Knowledge in Compressed Sensing

智力优势：压缩传感（CS）领域有望广泛地革新数字处理。 其关键思想是使用非自适应线性投影来获得一个有效的，减少了尺寸的信号或图像直接使用几个测量表示。 然而，在目前的实际CS算法，有两个限制，限制其在实际场景中的应用。 首先，CS中的大部分工作都处理确定性信号，并且不假设任何关于它们的先验知识。 然而，在许多应用中，除了其稀疏性之外，还可以获得关于潜在信号的附加先验信息。 先验信息可以确定性地或统计性地出现，例如，二阶统计。 我们的初步结果表明，利用它导致了显着的性能改善。 标准CS中的第二个约束是需要在感兴趣的信号允许稀疏表示的基础上执行重建，这降低了实际应用中的灵活性。 本研究通过探索如何在CS的一般框架中使用先验信息来解决这些限制，以实现更好的性能，即使在感兴趣的信号不允许稀疏表示的基础上进行重建。 此外，作为概念验证，我们将构建一个硬件演示系统，以展示所提出的技术在实际CS和真实信号中的可行性。更广泛的影响：压缩传感的进步可能会产生广泛的深远影响，包括光谱学，成像，通信以及消费电子产品的应用。 该项目将包括一个综合教育计划，涉及两个博士学位。学生和三名本科生，谁将被引入到这个新的领域。

Intellectual Merit: The field of compressive sensing (CS) promises to revolutionize digital processing broadly. The key idea is the use of nonadaptive linear projections to acquire an efficient, dimensionally reduced representation of a signal or image directly using just a few measurements. However, there are two limitations in current practical CS algorithms that constrain their application in practical scenarios. First, most of the work in CS deals with deterministic signals and does not assume any prior knowledge about them. In many applications, however, additional a priori information on the underlying signals is available, in addition to their sparsity. The a priori information may come either deterministically or statistically, e.g., through second order statistics. Our preliminary results show that exploiting it leads to a substantial performance improvement. The second constraint in standard CS is the need to perform reconstruction in a basis where the signal of interest admits a sparse representation, which reduces flexibility in practical applications. This research addresses these limitations by exploring how a priori information can be used in the general framework of CS to achieve improved performance, even when reconstruction is performed in a basis where the signal of interest does not admit a sparse representation. Furthermore, as a proof of concept, we will build a hardware demonstration system to show the feasibility of the proposed techniques in practical CS and with real-world signals.Broader Impact: Advances in compressive sensing may have a profound impact broadly, including applications in spectroscopy, imaging, communications, as well as consumer electronics. This project will include an integrated educational program involving two Ph.D. students and three undergraduate students, who will be introduced into this new field.